arXiv:2603.04378v1 Announce Type: cross Abstract: As Large Language Models (LLMs) transition into autonomous multi-agent ecosystems, robust minimax training becomes essential yet remains prone to instability when highly non-linear policies induce extreme local curvature in the inner maximization. Standard remedies that enforce global Jacobian bounds are overly conservative, suppressing sensitivity in all directions and inducing a large Price of Robustness. We introduce Adversarially-Aligned Jacobian Regularization (AAJR), a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions. We prove that AAJR yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation. Furthermore, we derive step-size conditions under which AAJR controls effective smoothness along optimization trajectories and ensures inner-loop stability. These results provide a structural theory for agentic robustness that decouples minimax stability from global expressivity restrictions.

arXiv:2602.14471v1 Announce Type: cross Abstract: Deploying large language model (LLM) agents in shared environments introduces a fundamental tension between individual alignment and collective stability: locally rational decisions can impose negative externalities that degrade system-level performance. We propose Socially-Weighted Alignment (SWA), a game-theoretic framework that modifies inference-time decision making by interpolating between an agent's private objective and an estimate of group welfare via a social weight $\lambda\in[0,1]$. In a shared-resource congestion game with $n$ agents and congestion severity $\beta$, we show that SWA induces a critical threshold $\lambda^*=(n-\beta)/(n-1)$ above which agents no longer have marginal incentive to increase demand under overload, yielding a phase transition from persistent congestion to stable operation near capacity. We further provide an inference-time algorithmic instantiation of SWA that does not require parameter updates or multi-agent reinforcement learning, and use a multi-agent simulation to empirically validate the predicted threshold behavior.